A common actuator in control systems is the DC motor. It directly provides rotary motion and, coupled with wheels or drums and cables, can provide translational motion. The electric equivalent circuit

of the armature and the free-body diagram of the rotor are shown in the following figure R dw dt Armature circuit L be Rotor Figure Q9 - Electric equivalent circuit The equations for an armature-controlled DC motor are as follow di L+Ri= -Kew+ v(t) dt + cw-Kri where w = = Fixed field de dt where the motor's current is i and its rotational velocity is w. L, R, and I are the motor's inductance, resistance, and inertia; KT and Ke are the torque constant and back-emf constant; c is a viscous damping constant; and v(t) is the applied voltage. Use the values R = 0.8 0, L = 0.003 H, KT = 0.05 N-m/A, Ke=0.05 V-s/rad, c = 0, and I = 8 x 105 kg - m². Suppose the applied voltage is 20 V. Use symbolic calculations to obtain the motor's speed and current versus time for zero initial conditions. Choose a final time large enough to show the motor's speed becoming constant. [11 marks]